# Properties

 Label 102550r Number of curves 2 Conductor 102550 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("102550.r1")

sage: E.isogeny_class()

## Elliptic curves in class 102550r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.r2 102550r1 [1, 1, 1, -12975213, 17984116531] [] 2695680 $$\Gamma_0(N)$$-optimal
102550.r1 102550r2 [1, 1, 1, -15575588, 10261295781] [] 8087040

## Rank

sage: E.rank()

The elliptic curves in class 102550r have rank $$0$$.

## Modular form 102550.2.a.r

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} - 2q^{9} - q^{12} + 4q^{13} - q^{14} + q^{16} - 3q^{17} - 2q^{18} + 2q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 